Chapter 8, Problem 10RE

Quality Control In a certain factory, some machines are properly adjusted and some need adjusting. Technicians randomly inspect machines and make adjustments. Suppose that, of the machines that are properly adjusted on a particular day, 80% will also be properly adjusted the following day and 20% will need adjusting. Also, of the machines that need adjusting on a particular day, 30% will be properly adjusted the next day and 70% will still need adjusting.

a. Set up the $2\times 2$ stochastic matrix, with columns labeled P (properly adjusted) and N (need adjusting), that describes this situation.

b. If, initially, all the machines are properly adjusted, what percent will need adjusting after 2 days?

c. In the long run, what percent will be properly adjusted each day?